where \(F=\frac{1}{4}F_{\mu \nu }F^{\mu \nu }\) , \(G=\frac{1}{4}F_{\mu \nu }\)\(^{\star } F^{\mu \nu } \) , \(F_{\mu \nu }\)  is the electromagnetic field strength tensor and its dual is \(^{\star } F^{\mu \nu } =\frac{\epsilon _{\mu \nu \sigma \rho }F^{\sigma \rho }}{2\sqrt{-g})} \) . \(\epsilon _{\mu \nu \sigma \rho }\)  is the antisymmetric tensor and satisfies \(\epsilon _{\mu \nu \sigma \rho }\epsilon ^{\mu \nu \sigma \rho } =-4!\) . \(a=\frac{8\alpha ^2}{45m^4}\)  is the Euler-Heisenberg parameter, where \(\alpha \)  is the fine structure constant and \(m\)  is the electron mass. From the action, Magos and Bretón got a static spherically symmetric solution. The metric is given by [1]}
\(ds^2 = -F(r)dt^2 + \frac{1}{F(r)}dr^2 + r^2(d\theta ^2+\sin ^2\theta d\phi ^2),\) 
